ELEMENTS OF DIGITAL COMMUNICATIONS Instructor: Dr. Mustafa El-Halabi Fall 2020 Theory is the first term in the Taylor series expansion of practice. T. COVER 2 TABLE OF CONTENTS Page TABLE OF CONTENTS 2 LIST OF FIGURES 4 1 PULSE CODE MODULATION 7 1.1 Digital Versus Analog Communication . 7 1.1.1 Advantages of Digital Communications versus Analog Communications . 8 1.2 Formatting Textual Data . 9 1.3 Analog Pulse Modulation . 9 1.3.1 Pulse Amplitude Modulation (PAM) . 9 1.3.2 Pulse Width Modulation (PWM) and Pulse Position Modulation (PPM) . 11 1.4 Quantization . 12 1.4.1 Scalar Quantization . 12 1.4.2 Minimum Mean-Square Quantization Error (MMSQE) . 15 1.4.3 Uniform Quantization . 16 1.4.4 Quantization Noise . 17 1.4.5 Non-Uniform Quantization/Companding . 18 1.5 Pulse Code Modulation (PCM) . 22 1.5.1 Regenerative Repeaters . 23 1.6 Baseband Modulation . 24 1.6.1 PCM Waveforms Types . 24 1.6.2 Bit Rate, Bit Duration and Bandwidth in PCM . 26 1.7 Virtues, Limitations and Modifications of PCM . 27 1.8 Differential Pulse-Code Modulation (DPCM) . 28 1.9 Linear Prediction . 29 1.10 Delta Modulation (DM) . 32 1.10.1 Quantization Noise . 33 1.11 Time-Division Multiplexing (TDM) . 35 1.11.1 Frame Synchronization . 36 3 INFORMATION THEORY 38 3.1 Introduction . 38 3.2 Measures of Information . 38 3.3 Source Codes . 44 3.3.1 Fixed-Length Codes . 45 3.3.2 Variable-Length Codes . 46 3.4 Huffman Coding Algorithm . 48 3.5 Tunstall Codes . 50 3.6 Lempel-Ziv Coding Algorithm . 51 3.7 Channel Coding . 52 3.7.1 Capacity of Bandlimited Channels . 55 4 RECEIVER DESIGN FOR AWGN BASEBAND COMMUNICATION 56 4.1 Introduction . 56 4.2 Hypothesis Testing . 57 Copyright c 2020, Dr. Mustafa El-Halabi2 4.2.1 MAP Decision Rule . 57 4.2.2 ML Decision Rule . 58 4.2.3 Binary Hypothesis Testing . 58 4.2.4 Performance Measure: Probability of Error . 59 4.3 Demodulation and Detection for the AWGN Channel . 60 4.3.1 The Matched Filter . 61 4.3.2 Threshold Detector and Error Probability . 63 4.3.3 Optimizing the Error Performance . 65 4.3.4 Correlation Realization of the Matched Filter . 67 5 BANDPASS COMMUNICATION 69 5.1 Introduction . 69 5.2 Bandpass Modulation Schemes . 71 5.2.1 Binary Amplitude-Shift Keying (ASK) . 71 5.2.2 Binary Phase-Shift Keying (PSK) . 71 5.2.3 Quadriphase-Shift Keying (QPSK) . 71 5.2.4 Binary Frequency-Shift Keying (FSK) . 72 5.3 M-ary Digital Modulation Schemes . 73 5.3.1 M-ary Phase-Shift Keying . 73 5.3.2 M-ary Quadrature Amplitude Modulation (QAM) . 74 5.3.3 M-ary Frequency-Shift Keying . 75 5.4 Discrete Data Detection . 76 5.4.1 The Vector Channel Model . 76 5.4.2 The MAP and ML Detectors . 77 5.4.3 Decision Regions . 78 5.5 Gaussian Random Vectors . 79 5.6 The Vector AWGN Channel . 80 5.6.1 Interpretation of the Optimum Detector for the AWGN Channel . 83 5.6.2 The Matched-Filter Receiver . 84 6 COMMUNICATION THROUGH BANDLIMITED AWGN CHANNELS 88 6.1 Digital Transmission Through Bandlimited Channels. 88 6.2 Digital PAM Transmission Through Bandlimited Baseband Channels. 90 6.3 The Power Spectrum of Digitally Modulated Signals. 92 6.4 Signal Design For Bandlimited Channels . 94 6.4.1 Design of Bandlimited Signals for Zero ISI − The Nyquist Criterion . 95 3 4 LIST OF FIGURES Page 1.1 Flat-top sampling of a message signal. 10 1.2 Illustration of two different forms of pulse-time modulation for the case of a saw-tooth modulating wave. (a) Modulating wave and Pulse carrier. (c) PDM wave. (d) PPM wave. 11 1.3 Encoding and decoding of discrete sources, analog sequence sources, and waveform sources. 12 1.4 Quantization regions and representation points. 13 1.5 Uniform scalar quantizer. 16 1.6 4-Level uniform quantization. 17 1.7 (a) Midrise uniform quantizer. (b) Midtread uniform quantizer . 17 1.8 The effect of increasing the quantization levels on reconstructing an image. 19 1.9 3-bit non-uniform quantizer. (a) Laplacian pdf. (b) Input-output characteristic. 19 1.10 Comparison between uniform and non-uniform quantization for a speech voltage signal. 20 1.11 Companding of voice signal. ..